It is likely that the production rate of entangled photons in a non-linear material is proportional to the power of the pump and the non-linear material susceptibility (chi-2). Would anyone know if there are expressions for this dependency, or any other dependencies (incl. references)?
thank you, Neil
Provided the pump has an number N of photons who have a certain ensured property that allows them to pass through the non-linear medium, and the medium has a change C to entangle them I'd say your power is N*C of entangled photons.
However, why would you want to know the power of entangled photons?
Entangled photons are more useful when considered discretely, and not in bulk expressions alike power. The only book I ever found to divulge into this was by Landau and Lifshitz (I'd have to look up in my library which one it was). However the complexity of real life materials is quite substantial to determine these number exactly, you probably should refrain to a very specific frequency spectrum, in which case possible optical transitions within the material are simpler. This will give you the entanglement probability. From that, the rest follows. However, as how you have expressed your question, I still wonder if you are really looking for the total number of entangled photons and rather more to the generation of different frequencies? Perhaps some background info? Let me know if you need the landau reference
Dear Frederik,
Thank you for your response. It would seem reasonable to assume that the production rate is proportional to the rate of the pump photons, the chi(2) of the medium and probably the thickness of the medium. I cant think of any other independent variables. The unknown here is the constant of proportionality. Perhaps (to first order) i can get an estimate of this by making comparisons to generations of entangled photons in the optical, where most experiments are conducted. I'm interested in generating these photons in the mm-wave band. I've got L&L i can check that out.
What is your "change C" above defined as?
Best wishes,
Neil
When properly implemented as states constructed form basic solutions of Maxwell equation in geometric algebra formalism (see “Polarizations as states and their evolution in geometric algebra terms with variable complex plane” and “The geometric algebra lift of qubits via basic solutions of Maxwell equation” particularly available at ResearchGate), entangled photon creation rate is restricted only by the lab equipment photon registration rate.
could you reference the experiments which do this generation in the optical range? Than I can know better what you hope to achieve.
perhaps the best reference is Chapter 8 of Exploring Quantum Physics Through Hands-On Projects Paperback – 1 Feb 2012 by David Prutchi (Author), Shanni R. Prutchi (Author):
https://www.amazon.co.uk/Exploring-Quantum-Physics-Through-Projects/dp/1118140664
best wishes,
Neil
And what is this chapter about? As it is not a reference I can open
Dear Frederik, the chapter is about entangled photon pair production in the optical band and confirmation the existence of by a Bell test. Cheers, Neil
Here's a paper for bulk crystals: https://arxiv.org/abs/1003.3810
And for waveguides: https://www.osapublishing.org/josab/abstract.cfm?URI=josab-29-8-2199
Citations therein have more derivations in various situations.
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